Details

sample188.0ms

Algorithm

intervals

Results

53.0ms	165×	body	80	valid
22.0ms	299×	body	80	nan
9.0ms	27×	body	1280	valid
9.0ms	32×	body	640	valid
8.0ms	19×	body	1280	nan
7.0ms	22×	body	640	nan
4.0ms	23×	body	320	valid
2.0ms	13×	body	320	nan
1.0ms	9×	body	160	valid
1.0ms	4×	body	160	nan

simplify1.4s

Counts: 1 → 1

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b	(* (sqrt 2.0) t)
13.1b	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.3b	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite297.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`times-frac` `associate-l` `associate-/r*` `add-log-exp`
4×	`sqrt-div`
3×	`flip3--` `associate-r` `flip--`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate--l+` `associate-/r/` `cbrt-unprod` `unswap-sqr`
1×	`distribute-rgt-in` `sub-neg` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `diff-log` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 80

Calls

4 calls:

111.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
20.0ms	(* (sqrt 2.0) t)
70.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
91.0ms	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series2.8s

Counts

4 → 12

Calls

4 calls:

631.0ms	(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
51.0ms	(* (sqrt 2.0) t)
295.0ms	(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
1.8s	(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify1.2s

Counts: 92 → 92

prune479.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 5.2b

localize31.0ms

Local error

Found 4 expressions with local error:

3.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.4b	(/ (pow l 2) x)
10.0b	(/ (pow t 2) x)
26.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

48×	`times-frac`
40×	`add-sqr-sqrt`
39×	`add-cube-cbrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`associate-/l*`
14×	`add-exp-log`
8×	`associate-*r/` `add-cbrt-cube` `unpow2` `sqr-pow`
6×	`div-exp` `associate-/r*` `add-log-exp`
5×	`pow1`
4×	`flip3-+` `sqrt-div` `frac-add` `flip-+`
3×	`sqrt-prod`
2×	`cbrt-undiv` `pow-to-exp` `associate-+r+` `frac-2neg` `pow-exp` `clear-num` `div-inv`
1×	`+-commutative` `distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `sum-log`

Counts

4 → 130

Calls

4 calls:

23.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
17.0ms	(/ (pow l 2) x)
17.0ms	(/ (pow t 2) x)
18.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
35.0ms	(/ (pow l 2) x)
35.0ms	(/ (pow t 2) x)
278.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify1.0s

Counts: 142 → 142

prune713.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 2.6b

localize22.0ms

Local error

Found 4 expressions with local error:

1.8b	(+ (pow t 2) (/ l (/ x l)))
3.2b	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
10.0b	(/ (pow t 2) x)
26.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite120.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity` `times-frac`
23×	`add-sqr-sqrt`
22×	`add-cube-cbrt`
12×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-r/` `associate-/l` `add-log-exp`
6×	`add-cbrt-cube`
5×	`pow1` `flip3-+` `flip-+`
4×	`sqrt-div` `frac-add` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*` `sqrt-prod`
2×	`+-commutative` `associate-+r+` `sum-log`
1×	`cbrt-undiv` `distribute-rgt-in` `pow-to-exp` `rem-sqrt-square` `frac-2neg` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 93

Calls

4 calls:

46.0ms	(+ (pow t 2) (/ l (/ x l)))
37.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
9.0ms	(/ (pow t 2) x)
21.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+ (pow t 2) (/ l (/ x l)))
88.0ms	(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
41.0ms	(/ (pow t 2) x)
233.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify1.2s

Counts: 105 → 105

prune590.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 2.6b

localize37.0ms

Local error

Found 4 expressions with local error:

10.0b	(/ (pow t 2) x)
26.7b	(sqrt (+ (pow t 2) (/ l (/ x l))))
26.7b	(sqrt (+ (pow t 2) (/ l (/ x l))))
26.7b	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ l (/ x l)))) (sqrt (+ (pow t 2) (/ l (/ x l))))))))

rewrite288.0ms

Algorithm

rewrite-expression-head

Rules

28×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`sqrt-div`
24×	`add-cube-cbrt` `times-frac`
18×	`associate-*r/`
12×	`unpow-prod-down`
11×	`sqrt-prod`
9×	`add-exp-log` `flip3-+` `flip-+`
8×	`frac-add` `associate-/l*`
7×	`pow1`
6×	`add-cbrt-cube`
4×	`frac-times` `unpow2` `add-log-exp` `sqr-pow`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `div-exp` `associate-/r*`
2×	`associate-*l/` `distribute-lft-out`
1×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `div-inv`

Counts

4 → 104

Calls

4 calls:

17.0ms	(/ (pow t 2) x)
94.0ms	(sqrt (+ (pow t 2) (/ l (/ x l))))
112.0ms	(sqrt (+ (pow t 2) (/ l (/ x l))))
58.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ l (/ x l)))) (sqrt (+ (pow t 2) (/ l (/ x l))))))))

series409.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (pow t 2) x)
105.0ms	(sqrt (+ (pow t 2) (/ l (/ x l))))
79.0ms	(sqrt (+ (pow t 2) (/ l (/ x l))))
204.0ms	(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (/ l (/ x l)))) (sqrt (+ (pow t 2) (/ l (/ x l))))))))

simplify1.0s

Counts: 116 → 116

prune616.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.6b

regimes718.0ms

Accuracy

79% (4.9b remaining)

Error of 8.6b against oracle of 3.8b and baseline of 26.9b

bsearch1.2s

Steps

Iters	Range		Point
7	3.0783966031544776e+86	2.585853520598322e+88	7.98256088580057e+87
7	-8.306565202719034e-227	-2.9248605148198587e-228	-4.7009624549413075e-227
4	-3.6816475514719145e-161	-2.0046842802775192e-161	-2.1560292641881286e-161
10	-1.0435976634563935e+132	-2.5332016092690966e+116	-2.1586038471179753e+131

simplify644.0ms

end0.0ms

sample6.6s

Algorithm

intervals

Results

1.5s	10277×	body	80	nan
1.1s	5029×	body	80	valid
988.0ms	898×	body	1280	valid
534.0ms	635×	body	1280	nan
521.0ms	1020×	body	640	valid
300.0ms	718×	body	320	valid
281.0ms	604×	body	640	nan
237.0ms	347×	body	320	nan
104.0ms	335×	body	160	valid
36.0ms	189×	body	160	nan